Type 2, during installation, to a partition with a spurious type label, as recommended. Installation ran successfully. Previous versions didn't run into this issue.
Am looking at suggested link - thanks. The problem is the same.
Maybe I can mount the Puppy partition using the live CD?
Should I make the Puppy partition bootable with cfdisk? I deliberately left it non-bootable in case the live distro tried to write to it.
Is there a simple way to edit the appropriate GRUB file? Which file, what statement?
Seems there might be scope for the gurus to mod. some of the code? A simple upgrade procedure would be extremely welcome now that Puppy is becoming so well regarded.
I am trying to install Puppy as single partitions onto 'old' HDs to save the planet from even more landfill blight! This is the best distro that can do all the routine stuff that most people need most of the time. Barry, you are a genius - don't stop now!

Just a little progress - but not enough!
I used the CD to change the partition type to ext2 (83)with cfdisk, as it seemed that the installer had left it with its spurious assignment.
This yielded an Error 15, so I reinstalled the GRUB MBR, also using the live CD.
This time it booted with GRUB all the way through to a working # prompt, when it showed a message: can't start X, missing /usr/X11R6/bin/X.
This directory is inaccessible from the prompt, although everything seems to be in place from a live CD boot. Don't understand the significance of the message: can't mount usr_cram.fs on /usr.
What next?

Sadly, no further progress! Have tried all the usual tricks of hiding partitions and changing their ID, plus quite a lot of my own crazy notions, including trying to use the 'upgrade' option in the install script and swapping the CD from 1.0.4 to 1.0.5 (something does happen - not sure what).
From which you'll adduce that an 1.0.4 install works every time!
There IS a problem here, but it's way beyond my ability to discover what it might be, much less how to fix it.
More help, please....

This may not be the perfect solution, but if you have room on the hard drive...

Make 2 partitions. One for version 1.04 and one for 1.05.

Install 1.04 on the first partition with grub.

Install 1.05 on the second partition and do not install grub.

You can then modify grub on the 1.04 partition to boot either.

There seems to be some issues with grub in 1.05? Or perhaps user error in setting it up. Believe me, I've messed up my grub file a few times. Granted, I do not use Puppy's grub, but this may be a fix right now for you._________________I love it when a plan comes together

Thanks, dan; that's one solution that evaded me! [but it wouldn't work on some of the tiny HD s I'm trying to resurrect!]
Not much hair to tear out, but even less this week. Solution found:
http://www.murga.org/~puppy/viewtopic.php?p=18089#18089
but it doesn't address the global issue - something HAS changed.

Weird, or what?!
Finally caught up with earlier discussion about the 1.0.5 install bug and the /usr issue - not that I understood much of it. The topic seems to be liberally sprayed across this site and newcomers of all abilities would welcome efforts of the (already overworked!) moderators to draw it all together, complete with some definitive guidance.
Notwithstanding, none of that explains why the install succeeded for me when I detuned my HW???????????
New problem with GKDial, now. I read a little about it being old and decrepit. It worked on first use and was able to D/L a pile of stuff, but, subsequently, it refuse to work. Doesn't seem to be the double-entry ISP problem, though? Found the wvdial issue and was able to manually edit the config (when I found it!). Neophytes often find it difficult to discover which files need modifying, what permissions are needed and how to reset them (if permitted) and where they are located.
I'd like to switch entirely to something like Puppy for it's sheer speed, coding efficiency, intuitive interface and flexible booting options.
Are we comparing it with the proverbial piece of string or is it possible to predict how long it'll take to arrive at a 99% debugged release? Moving target?!